// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2012-2016 Gael Guennebaud <gael.guennebaud@inria.fr> // // This Source Code Form is subject to the terms of the Mozilla // Public License v. 2.0. If a copy of the MPL was not distributed // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. #define EIGEN_RUNTIME_NO_MALLOC #include "main.h" #include <limits> #include <Eigen/Eigenvalues> #include <Eigen/LU> template<typename MatrixType> void generalized_eigensolver_real(const MatrixType& m) { /* this test covers the following files: GeneralizedEigenSolver.h */ Index rows = m.rows(); Index cols = m.cols(); typedef typename MatrixType::Scalar Scalar; typedef std::complex<Scalar> ComplexScalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; MatrixType a = MatrixType::Random(rows,cols); MatrixType b = MatrixType::Random(rows,cols); MatrixType a1 = MatrixType::Random(rows,cols); MatrixType b1 = MatrixType::Random(rows,cols); MatrixType spdA = a.adjoint() * a + a1.adjoint() * a1; MatrixType spdB = b.adjoint() * b + b1.adjoint() * b1; // lets compare to GeneralizedSelfAdjointEigenSolver { GeneralizedSelfAdjointEigenSolver<MatrixType> symmEig(spdA, spdB); GeneralizedEigenSolver<MatrixType> eig(spdA, spdB); VERIFY_IS_EQUAL(eig.eigenvalues().imag().cwiseAbs().maxCoeff(), 0); VectorType realEigenvalues = eig.eigenvalues().real(); std::sort(realEigenvalues.data(), realEigenvalues.data()+realEigenvalues.size()); VERIFY_IS_APPROX(realEigenvalues, symmEig.eigenvalues()); // check eigenvectors typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal(); typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors(); VERIFY_IS_APPROX(spdA*V, spdB*V*D); } // non symmetric case: { GeneralizedEigenSolver<MatrixType> eig(rows); // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition //Eigen::internal::set_is_malloc_allowed(false); eig.compute(a,b); //Eigen::internal::set_is_malloc_allowed(true); for(Index k=0; k<cols; ++k) { Matrix<ComplexScalar,Dynamic,Dynamic> tmp = (eig.betas()(k)*a).template cast<ComplexScalar>() - eig.alphas()(k)*b; if(tmp.size()>1 && tmp.norm()>(std::numeric_limits<Scalar>::min)()) tmp /= tmp.norm(); VERIFY_IS_MUCH_SMALLER_THAN( std::abs(tmp.determinant()), Scalar(1) ); } // check eigenvectors typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType D = eig.eigenvalues().asDiagonal(); typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType V = eig.eigenvectors(); VERIFY_IS_APPROX(a*V, b*V*D); } // regression test for bug 1098 { GeneralizedSelfAdjointEigenSolver<MatrixType> eig1(a.adjoint() * a,b.adjoint() * b); eig1.compute(a.adjoint() * a,b.adjoint() * b); GeneralizedEigenSolver<MatrixType> eig2(a.adjoint() * a,b.adjoint() * b); eig2.compute(a.adjoint() * a,b.adjoint() * b); } // check without eigenvectors { GeneralizedEigenSolver<MatrixType> eig1(spdA, spdB, true); GeneralizedEigenSolver<MatrixType> eig2(spdA, spdB, false); VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues()); } } EIGEN_DECLARE_TEST(eigensolver_generalized_real) { for(int i = 0; i < g_repeat; i++) { int s = 0; CALL_SUBTEST_1( generalized_eigensolver_real(Matrix4f()) ); s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(s,s)) ); // some trivial but implementation-wise special cases CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(1,1)) ); CALL_SUBTEST_2( generalized_eigensolver_real(MatrixXd(2,2)) ); CALL_SUBTEST_3( generalized_eigensolver_real(Matrix<double,1,1>()) ); CALL_SUBTEST_4( generalized_eigensolver_real(Matrix2d()) ); TEST_SET_BUT_UNUSED_VARIABLE(s) } }